The main aim of the paper is to present an algorithm solve approximately initial value problems for a scalar non-linear fractional differential equation with generalized proportional derivative on finite interval. condition connected one sided Lipschitz right hand side part given equation. An iterative scheme, based appropriately defined mild lower and upper solutions, provided. Two monotone se...

We consider the stochastic linear complementarity problem (SLCP) involving a random matrix whose expectation matrix is positive semi-definite. We show that the expected residual minimization (ERM) formulation of this problem has a nonempty and bounded solution set if the expected value (EV) formulation, which reduces to the LCP with the positive semi-definite expectation matrix, has a nonempty ...

The aim of this note is to study convergence and convergence rates of the regularized solutions for the operator equation of Hammerstein type x + F2F1(x) = f in reflexive Banach spaces under the non-monotone perturbations F h 2 and F h 1 of the operators F2 and F1, respectively.

We study monotone simultaneous embeddings of upward planar digraphs, which are simultaneous embeddings where the drawing of each digraph is upward planar, and the directions of the upwardness of different graphs can differ. We first consider the special case where each digraph is a directed path. In contrast to the known result that any two directed paths admit a monotone simultaneous embedding...

In this paper we study the following nonlinear Maxwell’s equations εEt+σ(x, |E|)E = ∇×H+F, Ht+∇×E = 0, where σ(x, s) is a monotone graph of s. It is shown that the system has a unique weak solution. Moreover, the limit of the solution as ε → 0 converges to the solution of quasi-stationary Maxwell’s equations. AMS(MOS) Subject Classifications: 35K20, 35Q20.

This paper deals with a new class of nonlinear set valued implicit variational inclusion problems involving (A, η)-monotone mappings in 2-uniformly smooth Banach spaces. Semi-inner product structure has been used to study the (A, η)-monotonicity. Using the generalized resolvent operator technique and the semi-inner product structure, the approximation solvability of the proposed problem is inve...

A k-submodular function is a generalization of a submodular function, where the input consists of k disjoint subsets, instead of a single subset, of the domain. Many machine learning problems, including influence maximization with k kinds of topics and sensor placement with k kinds of sensors, can be naturally modeled as the problem of maximizing monotone k-submodular functions. In this paper, ...

In this paper, we continue to investigate the inexact hybrid proximal point algorithm proposed by Mashreghi and Nasri for equilibrium problems in Banach spaces. Under some classes of generalized monotone conditions, we prove that the sequence generated by the method is strongly convergent to a solution of the problem, which is closest to the initial iterate, in the sense of Bregman distance. As...

This paper presents a general heuristic bottom-up procedure for finding a least-cost solution tree of an AND/OR graph when the cost functions associated with the arcs are monotone. Since monotone cost functions are very general, the procedure is applicable to a very large number of problems. The procedure works for both cyclic and acyclic AND/OR graphs, and subsumes most of the known bottom-up ...

An evolution equation, arising in the study of the Dynamical Systems Method (DSM) for solving equations with monotone operators, is studied in this paper. The evolution equation is a continuous analog of the regularized Newton method for solving ill-posed problems with monotone nonlinear operators F . Local and global existence of the unique solution to this evolution equation are proved, appar...